Question 1025311
Let {{{ a }}} = pounds of Kona beans needed
Let {{{ b }}} = pounds of regular beans needed
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(1) {{{ a + b = 50 }}}
(2) {{{ ( 45a + 10b ) / 50 = 31 }}}
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(2) {{{ 45a + 10b = 31*50 }}}
(2) {{{ 45a + 10b = 1550 }}}
(2) {{{ 9a + 2b = 310 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 9a + 2b = 310 }}}
(1) {{{ -2a - 2b = -100 }}}
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{{{ 7a = 210 }}}
{{{ a = 30 }}}
and
(1) {{{ a + b = 50 }}}
(1) {{{ b = 20 }}}
30 pounds of Kona beans are needed
20 pounds of regular beans are needed
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check:
(2) {{{ ( 45*30 + 10*20 ) / 50 = 31 }}}
(2) {{{ ( 1350 + 200 ) / 50 = 31 }}}
(2) {{{ 1550 = 31*50 }}}
(2) {{{ 1550 = 1550 }}}
OK